Robust detection and tracking algorithms for time reversal matched field processing

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In time reversal, matched field processing (TR/MFP), the backscatter of a signal transmitted into an environment is recorded, delayed, energy normalized, and retransmitted into the medium. TR/MFP offers an alternative to traditional detectors, e.g. the matched filter in one dimensional signal processing and the matched field processing (MFP) in multidimensions. The difficulty with MFP is that the Green's function used to model the channel is not known and, therefore, has to be computed numerically. By its inherent nature, TR/MFP intrinsically derives the Green's function of the channel as long as the receiving transducer array provides an adequate sampling of the channel. A second advantage of TR/MFP lies in the productive treatment of the channel multipaths. As is generally known, multipath significantly affects the performance of traditional detectors and is considered to be a detrimental and a negative whose effects should be minimized. TR/MFP presents the opposite opportunity: multipath as a positive, the more the better. Though the technique of TR/MFP is not new, but a thorough theory of detection for this setting is lacking. Our initial work addresses this gap and proves analytically, we believe for the first time, the phenomena of super resolution focusing observed with TR/MFP. In this proposal, we seek to extend this analysis further to provide quantitative answers to the following questions: How can TR/MFP be used in classical signal processing applications, such as: (i) target detection in a rich cluttering environment; (ii) channel capacity enhancement and equalization in wireless communications by some form of space division multiple access (SDMA); and (iii) inverse tomographic problems to determine channel characteristics, to name a few. We will also investigate how good TR/MFP is for target localization, tracking, and identification? What are the fundamental limits of TR/MFP? How stationary does the channel have to be for accurate TR/MFP?